Relativistic Quantum Information
A
crucial question in any approach to quantum information processing
is: first, how are classical bits
encoded
physically in the quantum system, second, how are they then manipulated and,
third, how are they finally read out?
I'll describe a special information-theoretic property of
quantum field theories with holographic duals: the mutual informations among
arbitrary disjoint spatial regions A,B,C obey the inequality I(A:BC) >=
I(A:B)+I(A:C), provided entanglement entropies are given by the Ryu-Takayanagi
formula. Inequalities of this type are known as monogamy relations and are
characteristic of measures of quantum entanglement. This suggests that
correlations in holographic theories arise primarily from entanglement rather
The fundamental properties of quantum
information and its applications to computing and cryptography have been
greatly illuminated by considering information-theoretic tasks that are
provably possible or impossible within non-relativistic quantum mechanics. In this talk I describe a general framework
for defining tasks within (special) relativistic quantum theory and illustrate
it with examples from relativistic quantum cryptography.
We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the modedecompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories.
Recent analysis of closed timelike curves from an information-theoretic perspective has led to contradictory conclusions about their information-processing power. One thing is generally agreed upon, however, which is that if such curves exist, the quantum-like evolution they imply would be nonlinear, but the physical interpretation of such theories is still unclear. It is known that any operationally verifiable instance of a nonlinear, deterministic evolution on some set of pure states makes the density matrix inadequate for representing mixtures of those pure states.
Bases of orthonormal localized states are constructed in Rindler coordinates and applied to an Unruh detector with good time resolution and an accelerated rod-like array detector.
Using the Deutsch approach, we show that the no-cloning theorem can be circumvented in the presence of closed timelike curves, allowing the perfect cloning of a quantum state chosen randomly from a finite alphabet of states. Further, we show that a universal cloner can be constructed that when acting on a completely arbitrary qubit state, exceeds the no-cloning bound on fidelity.
An unsolved problem in relativistic quantum information
research is how to model efficient, directional quantum communication between
localised parties in a fully quantum field theoretical framework. We propose a
tractable approach to this problem based on calculating expectation values of
localized field observables in the Heisenberg Picture. We illustrate our
approach by analysing, and obtaining approximate analytical solutions to, the
problem of communicating quantum states between an inertial sender, Alice and
In the Unruh effect, long-distance correlations in a pure
quantum state cause accelerated observers to experience the state as a thermal
bath. We discuss a similar phenomenon for quantum states that contain
correlations between the distant future and the distant past. Examples include
Minkowski half-space with a static mirror and an eternal black hole with an
unusual global structure behind the horizon. The question of utilising the
future-past correlations in quantum information tasks is raised.
After an introduction to generalized uncertainty
principle(s), we study uncertainty relations as formulated in a crystal-like
universe, whose lattice spacing is of order of
Planck length. For Planckian energies, the uncertainty relation for
position and momenta has a lower bound equal to zero. Connections of this
result with 't Hooft's deterministic quantization proposal, and with double
special relativity are briefly presented. We then apply our formulae to